A rocket sled accelerates from rest on a level track with negligible air and rol

Question

A rocket sled accelerates from rest on a level track with negligible air and rolling resistances. The initial mass of the sled is M0 = 600 kg. The rocket initially contains 150 kg of fuel. The rocket motor burns fuel at constant rate m = 15 kg/s. Exhaust gases leave the rocket nozzle uniformly and axially at Ve = 2900 m/s relative to the nozzle, and the pressure is atmospheric. Find the maximum speed reached by the rocket sled. Calculate the maximum acceleration of the sled during the run. Answers: max speed = 830 m/s. max acceleration = 97 m/s2

Explanation / Answer

M dv/dt = u dm/dt integrating we get v = u ln(M/ m) max speed = 2900 * ln(600/450) = 834 m/s thus, max acc = 2900*15/450 = 97 m/s^2

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